Factor the expression. 4a ^3 + 15a ^2 - 4a?

4a ^3 + 15a ^2 - 4a
=a(4a ^2 + 15a - 4)
=a(4a ^2 +16a-a-4)
a(4a-1)(a+4)

= 4a³ + 15a² - 4a
= a(4a² + 15a - 4)
4a² + 15a = 4
a² + 15/4a = 1
a² + 15/8a = 1 + (15/8)²
a² + 15/8a = 64/64 + 225/64
(a + 15/8)² = 289/64
a + 15/8 = 17/8

2nd factor:
= a + 15/8 + 17/8
= a + 4

3rd factor:
= (4a² + 15a - 4)/(a + 4)
= 4a - 1

Answer: a(a + 4)(4a - 1) are the factors.

do basically as your hint states in that order strengthen and multiply -3a^2+15a-4(4a^2-12a+9)-a^2+a -3a^2+15a-16a^2+48a-36-a^2+a collect like words -20a^2+64a-36 ingredient -4(5a^2-16a+9) think of it is lowest yet im drained

4a^3 + 15a^2 - 4a
= a(4a^2 + 15a - 4)
= a(4a^2 + 16a - a - 4)
= a(4a - 1)(a + 4)

4a ^ 3 + 15a ^ 2 - 4a
=a(4a ^ 2 + 15a - 4)
=a(4a ^ 2 + 16a - a - 4)
=a[4a (a + 4) - (a + 4)]
=a(a + 4) (4a - 1)

4a^3 + 15a^2 - 4a
=3*Log(4a) + 2*log(15a) - Log(4a)
=2*Log(4a)+2*Log(15a)
suppose(a~1)
= 2*{Log(4)+Log(1) + Log(15) + Log(1)}
(Log(1) = 0)
=> 2*{2*Log(2)+Log(3*5)}

= 2*{2*Log(2) + Log(3) + Log(5)}
(Use log table to find the rest)

a(4a^2 + 15a - 4)
= a(4a^2 + 16a - 1a - 4)
= a{4a(a + 4) - 1(a + 4)}
= a (a + 4) (4a - 1)

a (4a² + 15a - 4)
a (4a - 1)(a + 4)

4a³ + 15a² - 4a

first you can factor out an a:
a(4a² + 15a - 4)

a(4a² + 16a - a - 4)

a[ 4a(a + 4) - (a + 4) ]

a[ (4a - 1)(a + 4) ]

a(4a - 1)(a + 4) <--answer

hope this helped!

a(4a² + 15a - 4) = a(a + 4)(4a - 1)